Finite Group DatabasebetaFinite Group Databasebeta| order | 9900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D9×D25 |
| unambiguous semidirect product | (D9×C25)⋊(C2×C11) |
| unambiguous semidirect product | (C9×D25)⋊(C2×C11) |
| unambiguous semidirect product | D225⋊(C2×C11) |
| Fitting, Hall | C9×C11×C25 ⋊ C22 |
| derived, Hall | C9×C25 ⋊ C22×C11 |
| Hall | C11×C25 ⋊ C2×D9 |
| Hall | C9×C11 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C11×D9 |
| Sylow | C9 ⋊ C2×C11×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D9×D25 |
| commutator, cosocle, hypocenter | C9×C25 | C22×C11 |
| Frattini | C3×C5 | D3×D5×C11 |
| Fitting | C9×C11×C25 | C22 |
| socle | C3×C5×C11 | D3×D5 |
| LCS | G ▷ C9×C25 | |
| UCS | C1 ◁ C11 | |
90 conjugacy classes of subgroups.
924 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9900, 27);